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www.tartley.com | ||
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susam.net
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| | | | | A tiny, stack-based, postfix canvas colouring language. | |
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mishadoff.com
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jiggerwit.wordpress.com
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| | | | | I received an email from Josef Urban this morning. His group has been using AI to find algorithms that generate the sequences found in the Sloane's Online Encyclopedia of Integer Sequences (OEIS). The input is a finite sequence of integers. The output is an algorithm that produces the same sequence of digits. Using AI, they... | |
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www.jeremykun.com
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| | | Problem: $ \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \dots = 1$ Solution: Problem: $ \frac{1}{3} + \frac{1}{9} + \frac{1}{27} + \dots = \frac{1}{2}$ Solution: Problem: $ \frac{1}{4} + \frac{1}{16} + \frac{1}{64} + \dots = \frac{1}{3}$ Solution: Problem: $ 1 + r + r^2 + \dots = \frac{1}{1-r}$ if $ r < 1$. Solution: This last one follows from similarity of the subsequent trapezoids: the right edge of the teal(ish) trapezoid has length $ r$, and so the right edge of the neighboring trapezoid, $ x$, is found by $ \frac{r}{1} = \frac{x}{r}$, and we see that it has length $ r^2$. | ||
